Question: Rewrite as a simplified fraction. ${0.7\overline{51} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 751.5151...\\ 10x &= 7.5151...\end{align*}}$ Subtracting the two equations, we have: ${990x = 744}$ ${x = \dfrac{744}{990}} $ ${x = \dfrac{124}{165}} $